The Diamond-Square algorithm is a common algorithm used for simple heightmaps on a square base. Like all simple heightmap algorithms, it cannot deal with overhangs on any part of the landscape. However, it is one of the best algorithms available for minimising recognisable artifacts on the surface, that point to an artificial origin for the terrain.

It is a refinement of the midpoint displacement algorithm – the 'square' of the algorithm's name – which produced blocky, squarish-looking results. Diamond square improves these results by also including diamonds as well as squares in the generated results. These diamonds are of course just squares rotated by 45 degrees, but their presence in random locations is sufficient to remove the squarish effect, and lend a much more natural feel to the landscape.

As a result, Diamond square is the most popular algorithm used for procedural content generation systems for terrain in virtual environments.

Both algorithms use the same basic approach. Start with a basic rectangle of any size, as the area to be shaped. Either assign random height values to the corners, or take the height values from existing terrain. Divide the rectangle into four other rectangles, of equal or very different volumes, does not matter. They do not however, overlap one another. Let the height values of unspecified corners of these rectangles be calculated from the mean values of the four corners of the parent rectangle divided by the mean of whichever corners of the parent fall along the edge of the subdivided rectangle, plus or minus one standard deviation.

Each subdivided rectangle is then further subdivided and the process is repeated again and again until no more subdivisions are possible. Diamond square differs only in that a random number of these rectangles are rotated 45 degrees relative to the others, and can overlap. They create just enough offset to blur the inherent blockiness of the midpoint algorithm.

Like all random heightmap algorithms, diamond square cannot be used to create specific terrain features. It's only real use is in truly random terrain within specified parameters, for procedually generated raw landscapes.

AlphaWorld is an artist?s 3D environment with a square landmass, sixty-five kilometres to a side. This gives it four thousand, two hundred and twenty five square kilometres of land ? more than some countries. All of this land is open for ActiveWorlds? paying members to build upon, almost anything they desire.

Reconstructing Cities in a DayA computer algorithm developed at the University of Washington uses hundreds of thousands of tourist photos to automatically reconstruct an entire city in about a day.

WARP: Accelerating Wireless Technology Development
Prior to 2006, any attempt at investigating wireless technology, developing a new algorithm for propagation, or even trying for a whole new standard, all shared one thing in common: The phenomenal expense for the research team.

The Omni-focusThe omni-focus is a camera system with the ability to function much like the human eye - capturing objects in its field of vision regardless of the distance, in perfect focus. It even adapts an algorithm from VR, in order to do so.

If you have ever played the original Zelda games, then you will be familiar with what Graal is. This top-down 2D world system uses an almost infinite combination of square areas one and two screens wide, which slot together to form a world.

World Review: Graal

Graal is an oddity. If you have ever played the original Zelda games, then you will be familiar with what Graal is. This top-down 2D world system uses an almost infinite combination of square areas one and two screens wide, which slot together to form a world.

Adding Immersion in Activeworlds: Simple NPCs without BotsOne of the problems with wandering through a massive persistent world that can be many hundreds of square miles across, is the silence of it. After a while, no matter how beautiful the landscape, how awe-inspiring the view, the sheer bleakness of it all is going to get to you. If you are wandering alone, and have seen no other human participants, then it all starts to feel like dressing for "apocalypse now".

Thirteenth Floor: World BuildingWhat was nice about the world-building method used in floor 13, was it did not cut off suddenly, like many if not most worldlets in modern times do. Usually you have a grid, of a set number of cells arranged into a square or rectangular shape. Up until the edge of that grid, everything seems normal, then suddenly all the trees, rocks, vegetation, man-made objects stop dead.

World Review: Marian's World

Marian's world is a little bit of an oddity really. It is a world in which everyone is female, and tither stands about talking, walks and talks, or drives cars and talks. There's nowhere to actually drive cars to, as the entire world is a hilly, swampy island of about one half a square mile, with only three treehouse structures on it, yet everyone has a convertable sports car, and only one set of clothes.

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